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<a href="_hypervolume_contribution_approximator_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment"> *</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> *</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> * \brief       Approximately determines the individual contributing the least</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * hypervolume.</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> *</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> *</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> *</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * \author      T.Voss, O.Krause</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * \date        2010-2016</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> *</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> *</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> *</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> *</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * (at your option) any later version.</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> *</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> *</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="comment"> */</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_DIRECTSEARCH_HYPERVOLUME_CONTRIBUTION_APPROXIMATOR_H</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="preprocessor">#define SHARK_ALGORITHMS_DIRECTSEARCH_HYPERVOLUME_CONTRIBUTION_APPROXIMATOR_H</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#include &lt;boost/cstdint.hpp&gt;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="preprocessor">#include &lt;<a class="code" href="_pareto_dominance_8h.html">shark/Algorithms/DirectSearch/Operators/Domination/ParetoDominance.h</a>&gt;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="preprocessor">#include &lt;<a class="code" href="_hypervolume_calculator_8h.html">shark/Algorithms/DirectSearch/Operators/Hypervolume/HypervolumeCalculator.h</a>&gt;</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="preprocessor">#include &lt;limits&gt;</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span> </div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a> {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment"></span> </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="comment">/// \brief Approximately determines the point of a set contributing the least hypervolume.</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="comment">///</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment">/// See K. Bringmann, T. Friedrich. Approximating the least hypervolume contributor: NP-hard in general, but fast in practice. Proc. of the 5th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2009), Vol. 5467 of LNCS, pages 6-20, Springer-Verlag, 2009.</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="comment">///</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment">/// The algorithm works by estimating a bounding box for every point that includes all its contribution volume and then draw</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span><span class="comment">/// sample inside the box to estimate which fraction of the box is covered by other points in the set.</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span><span class="comment">///</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="comment">/// The algorithm only implements the k=1 version of the smallest contribution. For the element A it returns holds the</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="comment">/// following guarantue: with probability of 1-delta, Con(A) &lt; (1+epsilon)Con(LC)</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment">/// where LC is true least contributor. Note that there are no error guarantuees regarding the returned value of the contribution:</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span><span class="comment">/// the algorithm stops when it is sure that the bound above holds, but depending on the setup, this might be very early.</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">///</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment">/// Note that, while on average the algorithm performs reasonable well, the upper run-time is not bounded by the number of elements or dimensionality.</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">/// When two points have nearly the same(or exactly the same) contribution</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment">/// the algorithm will run for many iterations, until the bound above holds. The same holds if the point with the smallest contribution</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment">/// has a very large potential contribution as many samples are required to establish that allmost all of the box is covered.</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment">///</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span><span class="comment">///\tparam random The type of the random for sampling random points.</span></div>
<div class="foldopen" id="foldopen00065" data-start="{" data-end="};">
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html">   65</a></span><span class="comment"></span><span class="keyword">struct </span><a class="code hl_struct" href="structshark_1_1_hypervolume_contribution_approximator.html" title="Approximately determines the point of a set contributing the least hypervolume.">HypervolumeContributionApproximator</a>{<span class="comment"></span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span><span class="comment">    /// \brief Models a point and associated information for book-keeping purposes.</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> VectorType&gt;</div>
<div class="foldopen" id="foldopen00068" data-start="{" data-end="};">
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html">   68</a></span>    <span class="keyword">struct </span><a class="code hl_struct" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html" title="Models a point and associated information for book-keeping purposes.">Point</a> {</div>
<div class="foldopen" id="foldopen00069" data-start="{" data-end="}">
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#ad816e86a38c7e0c3dc7d36aa0bf139b1">   69</a></span>        <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#ad816e86a38c7e0c3dc7d36aa0bf139b1">Point</a>( <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a359c315fa6267c52c26e2f8c38ed683a">point</a>, <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; reference ) </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        : <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a359c315fa6267c52c26e2f8c38ed683a">point</a>( <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a359c315fa6267c52c26e2f8c38ed683a">point</a> )</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#ae981a10ff5d4c192da3a158757f18f4a">sample</a>( <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a359c315fa6267c52c26e2f8c38ed683a">point</a>.size() )</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a51eda5e69958b276c275be215c419f59">boundingBox</a>( reference )</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a81fc3e2d54ce593ce0574c655599b769">boundingBoxVolume</a>( 0. )</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#ae36d121776c390ad855323652a5f5752">approximatedContribution</a>( 0. )</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a75083583cfc4757423940b54427d4077">contributionLowerBound</a>( 0. )</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#afb3ec574c5a3ba7145b528fca013142a">contributionUpperBound</a>( 0. )</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a60a555ba2f3b4e14d963a9a858968385">computedExactly</a>(false)</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a9f8ac928261ec33f124d69fba264fdf7">noSamples</a>( 0 )</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#af7e9428f5fbc31abfeffef2a0815b439">noSuccessfulSamples</a>( 0 )</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        {}</div>
</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span> </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a359c315fa6267c52c26e2f8c38ed683a">   82</a></span>        <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a359c315fa6267c52c26e2f8c38ed683a">point</a>;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#ae981a10ff5d4c192da3a158757f18f4a">   83</a></span>        <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#ae981a10ff5d4c192da3a158757f18f4a">sample</a>;</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a51eda5e69958b276c275be215c419f59">   84</a></span>        <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a51eda5e69958b276c275be215c419f59">boundingBox</a>;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#ae3dd0caa7d126c4f06f7ff68e9c1e5dc">   85</a></span>        std::vector&lt; typename std::vector&lt;Point&gt;::const_iterator &gt; <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#ae3dd0caa7d126c4f06f7ff68e9c1e5dc">influencingPoints</a>;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a81fc3e2d54ce593ce0574c655599b769">   87</a></span>        <span class="keywordtype">double</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a81fc3e2d54ce593ce0574c655599b769">boundingBoxVolume</a>;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#ae36d121776c390ad855323652a5f5752">   88</a></span>        <span class="keywordtype">double</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#ae36d121776c390ad855323652a5f5752">approximatedContribution</a>;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a75083583cfc4757423940b54427d4077">   89</a></span>        <span class="keywordtype">double</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a75083583cfc4757423940b54427d4077">contributionLowerBound</a>;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#afb3ec574c5a3ba7145b528fca013142a">   90</a></span>        <span class="keywordtype">double</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#afb3ec574c5a3ba7145b528fca013142a">contributionUpperBound</a>;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a60a555ba2f3b4e14d963a9a858968385">   91</a></span>        <span class="keywordtype">bool</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a60a555ba2f3b4e14d963a9a858968385">computedExactly</a>;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        </div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a9f8ac928261ec33f124d69fba264fdf7">   93</a></span>        std::size_t <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#a9f8ac928261ec33f124d69fba264fdf7">noSamples</a>;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#af7e9428f5fbc31abfeffef2a0815b439">   94</a></span>        std::size_t <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator_1_1_point.html#af7e9428f5fbc31abfeffef2a0815b439">noSuccessfulSamples</a>;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    };</div>
</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#a9171724d5683e143759001a10f9bbb2c">   97</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a9171724d5683e143759001a10f9bbb2c">m_startDeltaMultiplier</a>;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#a40c556d7c0d1176e67f795cb30abbcb7">   98</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a40c556d7c0d1176e67f795cb30abbcb7">m_multiplierDelta</a>;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#a47929916ab69b0e384479ae4c20cdb62">   99</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a47929916ab69b0e384479ae4c20cdb62">m_minimumMultiplierDelta</a>;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    </div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#a16d77f5544fdf01e8bfdd0427b3e00d3">  101</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a16d77f5544fdf01e8bfdd0427b3e00d3">m_gamma</a>;</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#a7f253b29cea34ab461913fdf1e77017d">  102</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a7f253b29cea34ab461913fdf1e77017d" title="The error probability.">m_errorProbability</a>; <span class="comment">///&lt;The error probability.</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#aa4ee55eed212e9d241500366342088d9">  103</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#aa4ee55eed212e9d241500366342088d9" title="The error bound.">m_errorBound</a>;  <span class="comment">///&lt;The error bound</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span><span class="comment"></span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span><span class="comment">    /// \brief C&#39;tor</span></div>
<div class="foldopen" id="foldopen00106" data-start="{" data-end="}">
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#aceb0bba3d66b599e4762a59008da544a">  106</a></span><span class="comment"></span>    <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#aceb0bba3d66b599e4762a59008da544a" title="C&#39;tor.">HypervolumeContributionApproximator</a>()</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    : <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a9171724d5683e143759001a10f9bbb2c">m_startDeltaMultiplier</a>( 0.1 )</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a40c556d7c0d1176e67f795cb30abbcb7">m_multiplierDelta</a>( 0.775 )</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a47929916ab69b0e384479ae4c20cdb62">m_minimumMultiplierDelta</a>( 0.2 )</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a16d77f5544fdf01e8bfdd0427b3e00d3">m_gamma</a>( 0.25 )</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a7f253b29cea34ab461913fdf1e77017d" title="The error probability.">m_errorProbability</a>(1.E-2)</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    , <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#aa4ee55eed212e9d241500366342088d9" title="The error bound.">m_errorBound</a>(1.E-2)</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    {}</div>
</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        </div>
<div class="foldopen" id="foldopen00115" data-start="{" data-end="}">
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">  115</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">delta</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a7f253b29cea34ab461913fdf1e77017d" title="The error probability.">m_errorProbability</a>;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    }</div>
</div>
<div class="foldopen" id="foldopen00118" data-start="{" data-end="}">
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#a32cfcca40e4510e996dd41c9e3b428e1">  118</a></span>    <span class="keywordtype">double</span>&amp; <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a32cfcca40e4510e996dd41c9e3b428e1">delta</a>(){</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a7f253b29cea34ab461913fdf1e77017d" title="The error probability.">m_errorProbability</a>;</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    }</div>
</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    </div>
<div class="foldopen" id="foldopen00122" data-start="{" data-end="}">
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#aaa63c8502accc68b992534217eb32169">  122</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#aaa63c8502accc68b992534217eb32169">epsilon</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#aa4ee55eed212e9d241500366342088d9" title="The error bound.">m_errorBound</a>;</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    }</div>
</div>
<div class="foldopen" id="foldopen00125" data-start="{" data-end="}">
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#a4bc48c99de5ede9fa446b9b65403b27e">  125</a></span>    <span class="keywordtype">double</span>&amp; <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a4bc48c99de5ede9fa446b9b65403b27e">epsilon</a>(){</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#aa4ee55eed212e9d241500366342088d9" title="The error bound.">m_errorBound</a>;</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    }</div>
</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    </div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Archive&gt;</div>
<div class="foldopen" id="foldopen00130" data-start="{" data-end="}">
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#afd86ee5e8fa2705b792017a024295c0c">  130</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#afd86ee5e8fa2705b792017a024295c0c">serialize</a>( Archive &amp; archive, <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> version ) {</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        archive &amp; BOOST_SERIALIZATION_NVP(<a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a9171724d5683e143759001a10f9bbb2c">m_startDeltaMultiplier</a>);</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        archive &amp; BOOST_SERIALIZATION_NVP(<a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a40c556d7c0d1176e67f795cb30abbcb7">m_multiplierDelta</a>);</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        archive &amp; BOOST_SERIALIZATION_NVP(<a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a47929916ab69b0e384479ae4c20cdb62">m_minimumMultiplierDelta</a>);</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        archive &amp; BOOST_SERIALIZATION_NVP(<a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a16d77f5544fdf01e8bfdd0427b3e00d3">m_gamma</a>);</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        archive &amp; BOOST_SERIALIZATION_NVP(<a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a7f253b29cea34ab461913fdf1e77017d" title="The error probability.">m_errorProbability</a>);</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        archive &amp; BOOST_SERIALIZATION_NVP(<a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#aa4ee55eed212e9d241500366342088d9" title="The error bound.">m_errorBound</a>);</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    }</div>
</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span><span class="comment"></span> </div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span><span class="comment">    /// \brief Determines the point contributing the least hypervolume to the overall set of points.</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span><span class="comment">    /// \param [in] points pareto front of points</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span><span class="comment">    /// \param [in] k The number of points to select.</span></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span><span class="comment">    /// \param [in] reference The reference point to consider for calculating individual points&#39; contributions.</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Set,<span class="keyword">class</span> VectorType&gt;</div>
<div class="foldopen" id="foldopen00145" data-start="{" data-end="}">
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#a5d9f9832db56f043a2f389ad5a386b55">  145</a></span>    std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt; <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a5d9f9832db56f043a2f389ad5a386b55" title="Determines the point contributing the least hypervolume to the overall set of points.">smallest</a>(Set <span class="keyword">const</span>&amp; points, std::size_t k, <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; reference)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(points.size() &gt;= k, <span class="stringliteral">&quot;There must be at least k points in the set&quot;</span>);</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(k == 1, <span class="stringliteral">&quot;Not implemented for k != 1&quot;</span>);</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>                </div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        std::vector&lt; Point&lt;VectorType&gt; &gt; front;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span> <span class="keyword">const</span>&amp; point: points) {</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>            front.emplace_back( point, reference );</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        }</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        computeBoundingBoxes( front );</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>        </div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        std::vector&lt; typename std::vector&lt; Point&lt;VectorType&gt; &gt;::iterator &gt; activePoints;</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span> it = front.begin(); it != front.end(); ++it ) {</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>            activePoints.push_back( it );</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        }</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        </div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        <span class="keyword">auto</span> <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a5d9f9832db56f043a2f389ad5a386b55" title="Determines the point contributing the least hypervolume to the overall set of points.">smallest</a> = computeSmallest(activePoints, front.size());</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        </div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt; result(1);</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        result[0].key = <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a5d9f9832db56f043a2f389ad5a386b55" title="Determines the point contributing the least hypervolume to the overall set of points.">smallest</a>-&gt;approximatedContribution;</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        result[0].value = <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a5d9f9832db56f043a2f389ad5a386b55" title="Determines the point contributing the least hypervolume to the overall set of points.">smallest</a>-front.begin();</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    }</div>
</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        </div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <span class="comment"></span></div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span><span class="comment">    /// \brief Returns the index of the points with smallest contribution.</span></div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span><span class="comment">    /// As no reference point is given, the extremum points can not be computed and are never selected.</span></div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span><span class="comment">    /// \param [in] points The set \f$S\f$ of points from which to select the smallest contributor.</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span><span class="comment">    /// \param [in] k The number of points to select.</span></div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Set&gt;</div>
<div class="foldopen" id="foldopen00176" data-start="{" data-end="}">
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution_approximator.html#a6d452284d5ae1b104a992ce605e03baa">  176</a></span>    std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt; <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a6d452284d5ae1b104a992ce605e03baa" title="Returns the index of the points with smallest contribution.">smallest</a>(Set <span class="keyword">const</span>&amp; points, std::size_t k)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(points.size() &gt;= k, <span class="stringliteral">&quot;There must be at least k points in the set&quot;</span>);</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(k == 1, <span class="stringliteral">&quot;Not implemented for k != 1&quot;</span>);</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        </div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        <span class="comment">//find reference point as well as points with lowest function value</span></div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        std::vector&lt;std::size_t&gt; minIndex(points[0].size(),0);</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>        RealVector minVal = points[0];</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        RealVector reference=points[0];</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        <span class="keywordflow">for</span>(std::size_t i = 1; i != points.size(); ++i){</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>            noalias(reference) = max(reference,points[i]);</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>            <span class="keywordflow">for</span>(std::size_t j = 0; j != minVal.size(); ++j){</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>                <span class="keywordflow">if</span>(points[i](j)&lt; minVal[j]){</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>                    minVal[j] = points[i](j);</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>                    minIndex[j]=i;</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>                }</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>            }</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        }</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        </div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        std::vector&lt; Point&lt;RealVector&gt; &gt; front;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        front.reserve( points.size() );</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span> <span class="keyword">const</span>&amp; point: points){</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>            front.emplace_back( point, reference );</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        }</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        computeBoundingBoxes( front );</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>        </div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        std::vector&lt;std::vector&lt; Point&lt;RealVector&gt; &gt;::iterator &gt; activePoints;</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span> it = front.begin(); it != front.end(); ++it ) {</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>            <span class="keywordflow">if</span>(std::find(minIndex.begin(),minIndex.end(),it-front.begin()) != minIndex.end())</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>                <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>            <span class="comment">//~ //check whether point is on the boundary -&gt; least contributor</span></div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>            <span class="comment">//~ for(std::size_t j = 0; j != minVal.size(); ++j){</span></div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>                <span class="comment">//~ if(it-&gt;point[j] == reference[j]){</span></div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>                    <span class="comment">//~ return std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt;(1,{0.0,it-front.begin()});</span></div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>                <span class="comment">//~ }</span></div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>            <span class="comment">//~ }</span></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>            activePoints.push_back( it );</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>        </div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>        }</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>        </div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>        </div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>        <span class="keyword">auto</span> <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a5d9f9832db56f043a2f389ad5a386b55" title="Determines the point contributing the least hypervolume to the overall set of points.">smallest</a> = computeSmallest(activePoints, front.size());</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>        std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt; result(1);</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>        result[0].key = <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a5d9f9832db56f043a2f389ad5a386b55" title="Determines the point contributing the least hypervolume to the overall set of points.">smallest</a>-&gt;approximatedContribution;</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        result[0].value = <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a5d9f9832db56f043a2f389ad5a386b55" title="Determines the point contributing the least hypervolume to the overall set of points.">smallest</a>-front.begin();</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    }</div>
</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span> </div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    </div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Set&gt;</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>    <span class="keyword">typename</span> Set::value_type computeSmallest(Set&amp; activePoints, std::size_t n)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>        <span class="keyword">typedef</span> <span class="keyword">typename</span> Set::value_type SetIter;</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>        <span class="comment">//compute initial guess for delta</span></div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        <span class="keywordtype">double</span> <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">delta</a> = 0.;</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>        <span class="keywordflow">for</span>( <span class="keyword">auto</span> it = activePoints.begin(); it != activePoints.end(); ++it )</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>            <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">delta</a> = std::max( <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">delta</a>, (*it)-&gt;boundingBoxVolume );</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">delta</a> *= <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a9171724d5683e143759001a10f9bbb2c">m_startDeltaMultiplier</a>;</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        </div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> round = 0;</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        <span class="keywordflow">while</span>( <span class="keyword">true</span> ) {</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>            round++;</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>            </div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>            <span class="comment">//check whether we spent so much time on sampling that computing the real volume is not much more expensive any more.</span></div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>            <span class="comment">//this guarantuees convergence even in cases that two points have the same hyper volume.</span></div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>            <a class="code hl_define" href="_open_m_p_8h.html#a8a63d79e2c3625260e6092d933f21a98" title="Set of macros to help usage of OpenMP with Shark.">SHARK_PARALLEL_FOR</a>(<span class="keywordtype">int</span> i = 0; i &lt; (int)activePoints.size(); ++i){</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>                <span class="keywordflow">if</span>(shouldCompute(*activePoints[i])){</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>                    computeExactly(*activePoints[i]);</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>                }</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>            }</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>            </div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>            <span class="comment">//sample all active points so that their individual deviations are smaller than delta</span></div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>            <span class="keywordflow">for</span>( <span class="keyword">auto</span> point: activePoints )</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>                sample( *point, round, <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">delta</a>, n );</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span> </div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>            <span class="comment">//find the current least contributor</span></div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>            <span class="keyword">auto</span> minimalElement = std::min_element(</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>                activePoints.begin(),activePoints.end(),</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>                [](SetIter <span class="keyword">const</span>&amp; a, SetIter <span class="keyword">const</span>&amp; b){return a-&gt;approximatedContribution &lt; b-&gt;approximatedContribution;}</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>            );</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span> </div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>            <span class="comment">//section 3.4.1: push the least contributor: decrease its delta further to have a chance to end earlier.</span></div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>            <span class="keywordflow">if</span>( activePoints.size() &gt; 2 ) {</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>                sample( **minimalElement, round, <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a47929916ab69b0e384479ae4c20cdb62">m_minimumMultiplierDelta</a> * <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">delta</a>, n );</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>                minimalElement = std::min_element(</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>                    activePoints.begin(),activePoints.end(),</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>                    [](SetIter <span class="keyword">const</span>&amp; a, SetIter <span class="keyword">const</span>&amp; b){return a-&gt;approximatedContribution &lt; b-&gt;approximatedContribution;}</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>                );</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>            }</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span> </div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>            <span class="comment">//remove all points whose confidence interval does not overlap with the current minimum any more.</span></div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>            <span class="keywordtype">double</span> erase_level = (*minimalElement)-&gt;contributionUpperBound;</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>            <span class="keyword">auto</span> erase_start = std::remove_if(</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>                activePoints.begin(),activePoints.end(),</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>                [=](SetIter <span class="keyword">const</span>&amp; point){return point-&gt;contributionLowerBound &gt; erase_level;}</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>            );</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>            activePoints.erase(erase_start,activePoints.end());</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>            </div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>            <span class="comment">//if the set only has one point left, we are done.</span></div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>            <span class="keywordflow">if</span>(activePoints.size() == 1)</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>                <span class="keywordflow">return</span> activePoints.front();</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span> </div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>            <span class="comment">// stopping conditions: have we reached the desired accuracy? </span></div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>            <span class="comment">// for this we need to know:</span></div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>            <span class="comment">// 1. contribution for all points are bounded above 0</span></div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>            <span class="comment">// 2. upperBound(LC) &lt; (1+epsilon)*lowerBound(A) for all A</span></div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>            <span class="keywordtype">double</span> d = 0;</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>            <span class="keywordflow">for</span>( <span class="keyword">auto</span> it = activePoints.begin(); it != activePoints.end(); ++it ) {</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>                <span class="keywordflow">if</span>( it == minimalElement )</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>                    <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>                <span class="keywordtype">double</span> nom = (*minimalElement)-&gt; contributionUpperBound;</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>                <span class="keywordtype">double</span> den = (*it)-&gt;contributionLowerBound;</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>                <span class="keywordflow">if</span>( den &lt;= 0. )</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>                    d = std::numeric_limits&lt;double&gt;::max();</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>                    d = std::max(d,nom/den);</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>            }</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>            </div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>            <span class="comment">//if the stopping condition is fulfilled, return the minimal element</span></div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>            <span class="keywordflow">if</span>(d &lt; 1. + <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#aa4ee55eed212e9d241500366342088d9" title="The error bound.">m_errorBound</a>){</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>                <span class="keywordflow">return</span> *minimalElement;</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>            }</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>            </div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>            <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">delta</a> *= <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a40c556d7c0d1176e67f795cb30abbcb7">m_multiplierDelta</a>;</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>        }</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>    }</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>    <span class="comment"></span></div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span><span class="comment">    /// \brief Samples in the bounding box of the supplied point until a pre-defined threshold is reached.</span></div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span><span class="comment">    /// \param [in] point Iterator to the point that should be sampled.</span></div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span><span class="comment">    /// \param [in] r The current round.</span></div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span><span class="comment">    /// \param [in] delta The delta that should be reached.</span></div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span><span class="comment">    /// \param [in] n the total number of points in the front. Required for proper calculation of bounds</span></div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> VectorType&gt;</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>    <span class="keywordtype">void</span> sample( Point&lt;VectorType&gt;&amp; point, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r, <span class="keywordtype">double</span> <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">delta</a>, std::size_t n )<span class="keyword">const</span>{</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>        <span class="keywordflow">if</span>(point.computedExactly) <span class="keywordflow">return</span>;<span class="comment">//spend no time on points that are computed exactly</span></div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        </div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>        <span class="keywordtype">double</span> logFactor = std::log( 2. * n * (1. + <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a16d77f5544fdf01e8bfdd0427b3e00d3">m_gamma</a>) / (<a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a7f253b29cea34ab461913fdf1e77017d" title="The error probability.">m_errorProbability</a> * <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a16d77f5544fdf01e8bfdd0427b3e00d3">m_gamma</a>) );</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>        <span class="keywordtype">double</span> logR = std::log( <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>( r ) );</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>        <span class="comment">//compute how many samples we need until the bound of the current box is smaller than delta</span></div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>        <span class="comment">//this is formula (3) in the paper when used in an equality &lt; delta and solving for noSamples</span></div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>        <span class="comment">//we add +1 to ensure that the inequality holds.</span></div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>        <span class="keywordtype">double</span> thresholdD= 1.0+0.5 * ( (1. + <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a16d77f5544fdf01e8bfdd0427b3e00d3">m_gamma</a>) * logR + logFactor ) * <a class="code hl_function" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63" title="Calculates x^2.">sqr</a>( point.boundingBoxVolume / <a class="code hl_function" href="structshark_1_1_hypervolume_contribution_approximator.html#a57c159dc8900f273d0f0fd58147ee6d4">delta</a> );</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>        std::size_t threshold = <span class="keyword">static_cast&lt;</span>std::size_t<span class="keyword">&gt;</span>(thresholdD);</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>        <span class="comment">//sample points inside the box of the current point</span></div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>        <span class="keywordflow">for</span>( ; point.noSamples &lt; threshold; point.noSamples++ ) {</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>            <span class="comment">//sample a point inside the box</span></div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>            point.sample.resize(point.point.size());</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>            <span class="keywordflow">for</span>( <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i &lt; point.sample.size(); i++ ) {</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>                point.sample[ i ] =  <a class="code hl_function" href="namespaceshark_1_1random.html#a18f302ea18f70835c59935973ba8ea84" title="Draws a number uniformly in [lower,upper] by drawing random numbers from rng.">random::uni</a>(<a class="code hl_variable" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">random::globalRng</a>, point.point[ i ], point.boundingBox[ i ] );</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>            }</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>            ++point.noSamples;</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>            <span class="comment">//check if the point is not dominated by any of the influencing points</span></div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>            <span class="keywordflow">if</span>( !isPointDominated( point.influencingPoints, point.sample ) )</div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>                point.noSuccessfulSamples++;</div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>        }</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span> </div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>        <span class="comment">//current best guess for volume: fraction of accepted points inside the box imes the volume of the box. (2) in the paper</span></div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>        point.approximatedContribution = (point.boundingBoxVolume * point.noSuccessfulSamples) /  point.noSamples;</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>        <span class="comment">//lower and upper bounds for the best guess: with high probability it will be in this region. (3) in the paper.</span></div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>        <span class="keywordtype">double</span> deltaReached = std::sqrt( 0.5 * ((1. + <a class="code hl_variable" href="structshark_1_1_hypervolume_contribution_approximator.html#a16d77f5544fdf01e8bfdd0427b3e00d3">m_gamma</a>) * logR+ logFactor ) / point.noSamples ) * point.boundingBoxVolume;</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>        point.contributionLowerBound = point.approximatedContribution - deltaReached;</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>        point.contributionUpperBound = point.approximatedContribution + deltaReached;</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>    }</div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>    <span class="comment"></span></div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span><span class="comment">    /// \brief Checks whether a point is dominated by any point in a given set.</span></div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span><span class="comment">    /// \tparam Set The type of the set of points.</span></div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span><span class="comment">    /// \param [in] set The set of individuals to check the sampled point against.</span></div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span><span class="comment">    /// \param [in] point Point to test</span></div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span><span class="comment">    /// \returns true if the point was non-dominated</span></div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Set, <span class="keyword">typename</span> VectorType&gt;</div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>    <span class="keywordtype">bool</span> isPointDominated( Set <span class="keyword">const</span>&amp; set, <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; point )<span class="keyword">const</span>{</div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>        </div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>        <span class="keywordflow">for</span>( <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i &lt; set.size(); i++ ) {</div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>            <a class="code hl_enumeration" href="namespaceshark.html#a9dd514911f0c8ea5d1e7d9c5da198c45" title="Result of comparing two objective vectors w.r.t. Pareto dominance.">DominanceRelation</a> rel = <a class="code hl_function" href="namespaceshark.html#a7b70e475fc3fb175cdfe5f2130d8c2cd" title="Pareto dominance relation for two objective vectors.">dominance</a>(set[i]-&gt;point, point);</div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>            <span class="keywordflow">if</span> (rel == <a class="code hl_enumvalue" href="namespaceshark.html#a9dd514911f0c8ea5d1e7d9c5da198c45a6b8a8f1e70649e457e42340e307475c3">LHS_DOMINATES_RHS</a>)</div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>        }</div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>    }</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span><span class="comment"></span> </div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span><span class="comment">    /// \brief Computes bounding boxes and their volume for the range of points defined by the iterators.</span></div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span><span class="comment">    /// \param [in] set The set of individuals.</span></div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Set&gt;</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>    <span class="keywordtype">void</span> computeBoundingBoxes(Set&amp; set )<span class="keyword">const</span>{</div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span> it = set.begin(); it != set.end(); ++it ) {</div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>            <span class="keyword">auto</span>&amp; p1 = *it;</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>            <span class="comment">//first cut the bounding boxes on sides that are completely covered by other points</span></div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>            <span class="keywordflow">for</span>(<span class="keyword">auto</span> itt = set.begin(); itt != set.end(); ++itt ) {</div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span> </div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>                <span class="keywordflow">if</span>( itt == it )</div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>                    <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span> </div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>                <span class="keyword">auto</span>&amp; p2 = *itt;</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span> </div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>                <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> coordCounter = 0;</div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>                <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> coord = 0;</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>                <span class="keywordflow">for</span>( <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> o = 0; o &lt; p1.point.size(); o++ ) {</div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>                    <span class="keywordflow">if</span>( p2.point[ o ] &gt; p1.point[ o ] ) {</div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>                        coordCounter++;</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>                        <span class="keywordflow">if</span>( coordCounter == 2 )</div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>                            <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>                        coord = o;</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>                    }</div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>                }</div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span> </div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>                <span class="keywordflow">if</span>( coordCounter == 1 &amp;&amp; p1.boundingBox[ coord ] &gt; p2.point[ coord ] )</div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>                    p1.boundingBox[ coord ] = p2.point[ coord ];</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>            }</div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>            </div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>            <span class="comment">//compute volume of the box</span></div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>            it-&gt;boundingBoxVolume = 1.;</div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>            <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0 ; i &lt; it-&gt;boundingBox.size(); i++ ) {</div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>                it-&gt;boundingBoxVolume *= it-&gt;boundingBox[ i ] - it-&gt;point[ i ];</div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>            }</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span> </div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>            <span class="comment">//find all points that are partially covering this box</span></div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>            <span class="keywordflow">for</span>(<span class="keyword">auto</span> itt = set.begin(); itt != set.end(); ++itt ) {</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>                <span class="keywordflow">if</span>( itt == it )</div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>                    <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span> </div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>                <span class="keywordtype">bool</span> isInfluencing = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>                <span class="keywordflow">for</span>( <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i &lt; it-&gt;point.size(); i++ ) {</div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>                    <span class="keywordflow">if</span>( itt-&gt;point[ i ] &gt;= it-&gt;boundingBox[ i ] ) {</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>                        isInfluencing = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>                        <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>                    }</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>                }</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>                <span class="keywordflow">if</span>( isInfluencing ) {</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>                    it-&gt;influencingPoints.push_back( itt );</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>                }</div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>            }</div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>        }</div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>    }</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> VectorType&gt;</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>    <span class="keywordtype">bool</span> shouldCompute(Point&lt;VectorType&gt; <span class="keyword">const</span>&amp; point)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>        <span class="comment">//we do not compute if it is already computed</span></div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>        <span class="keywordflow">if</span>(point.computedExactly) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>        std::size_t numPoints = point.influencingPoints.size();</div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>        <span class="comment">//point is on its own no need to sample.</span></div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>        <span class="keywordflow">if</span>(numPoints == 0) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>        std::size_t numObjectives = point.point.size();</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>        <span class="comment">//runtime already spend on point</span></div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>        <span class="keywordtype">double</span> time = (double)point.noSamples * numObjectives;</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>        </div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>        <span class="comment">//estimate of algo run time</span></div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span>        <span class="keywordtype">double</span> algoRunTime = 0.03 * numObjectives * numObjectives * std::pow(numPoints, numObjectives * 0.5 );</div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span>        <span class="keywordflow">return</span> time &gt; algoRunTime;</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>    }</div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span>    </div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> VectorType&gt;</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span>    <span class="keywordtype">void</span> computeExactly(Point&lt;VectorType&gt;&amp; point)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno">  430</span>        std::size_t numPoints = point.influencingPoints.size();</div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>        <span class="comment">//compute volume of the points inside the box</span></div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span>        std::vector&lt;VectorType&gt; transformedPoints(numPoints);</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>        <span class="keywordflow">for</span>(std::size_t j = 0; j != numPoints; ++j){</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span>            transformedPoints[j] = max(point.influencingPoints[j]-&gt;point, point.point);</div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span>        }</div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno">  436</span>        HypervolumeCalculator vol;</div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span>        <span class="keywordtype">double</span> volume = point.boundingBoxVolume - vol(transformedPoints, point.boundingBox);</div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>        point.computedExactly = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span>        point.contributionLowerBound = volume;</div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>        point.contributionUpperBound = volume;</div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>        point.approximatedContribution = volume;</div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span>    }</div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span>};</div>
</div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno">  444</span>}</div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno">  445</span> </div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span><span class="preprocessor">#endif</span></div>
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